School Commit Init

Anul 1/Semestrul 1/Fundamentals of Programming/a4-912-Cujba-Daniel/dynamic_programming.py

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+# 3.Given the set of positive integers S, partition this set into two subsets S1 and S2 so that the difference between 
+# the sum of the elements in S1 and S2 is minimal. For example, for set S = { 1, 2, 3, 4, 5 }, 
+# the two subsets could be S1 = { 1, 2, 4 } and S2 = { 3, 5 }. Display at least one of the solutions.
+
+def naive(s,s1,s2):
+    if len(s)==0:
+        return [s1,s2]
+    x=s.pop()
+    x1=naive(s.copy(),s1+[x],s2)
+    x2=naive(s.copy(),s1,s2+[x])
+    if abs(sum(x1[0])-sum(x1[1]))<abs(sum(x2[0])-sum(x2[1])):
+        return x1
+    else:
+        return x2
+
+def naive_imp(s):
+    return naive(s.copy(),[],[])
+
+def dynamic(s):
+    half_sum=sum(s)//2+1
+    data=[[False,[]] for _ in range(half_sum)]
+    data[0]=[True,[]]
+    for i in s:
+        for j in range(half_sum):
+            if data[j][0] and j+i<half_sum and (i not in data[j][1]):
+                data[j+i]=[True,data[j][1]+[i]]
+    for i in range(half_sum-1,0,-1):
+        if data[i][0]:
+            return [data[i][1],[j for j in s if j not in data[i][1]]]
+
+
+if __name__ == "__main__":
+    s=[1,2,3,4,5]
+    print("Naive: {}".format(naive_imp(s)))
+    print("Dynamic: {}".format(dynamic(s)))